In contemporary web browsers, favicons are prominently displayed in the browser's UI. As such they have become an integral aspect of creating a site that looks professional. More importantly, they allow users to identify a website from a host of tabs or bookmarks. Alas only a third of web pages (based only on my bookmarks list, admittedly) offer a favicon.

What your favicon looks like is less relevant than having something distinctive. Favicons should trigger recognition, and need not stand up to examination.